数理逻辑教程
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作者(法)Y.Choquet-Bruhat(Y.肖凯-布吕埃)
出版社世界图书出版公司
ISBN9787510086304
出版时间2015-03
版次1
装帧平装
开本16开
纸张胶版纸
页数599页
定价98元
上书时间2024-08-02
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基本信息
书名:数理逻辑教程
定价：98.00元
作者:(法)Y.Choquet-Bruhat(Y.肖凯-布吕埃)
出版社：世界图书出版公司
出版日期：2015-03-01
ISBN：9787510086304
字数：
页码：599
版次：1
装帧：平装
开本：16开
商品重量：
编辑推荐
《数理逻辑教程(英文)》由世界图书出版公司北京公司出版。
内容提要
本书分为2卷,卷1977年初版，之后7次重印或修订。第2卷也在原来的基础上做了不少改进，增加了一部分内容讲述主纤维丛上的连通，包括完整，协变倒数，曲率，线性连通，示性类和不变曲率积分。书中有部分内容完全重写，增加了不少例子和练习，使得内容更加容易理解。目次：分析基本观点；Banach空间上的微积分；微分流行、有限维的例子；流形上的积分；Riemannian流形，K?hlerian流形；分布；微分流形，无限维的例子。读者对象：适用于物理、数学专业研究人员和学生.
目录
Acknowledgements Interdependence scheme for the chapters Introduction Recommended reading CHAPTER 0.PREREQUISITES CHAPTER 1.BEGINNING MATHEMATICAL LOGIC 1.General considerations 2.Structures and formal languages 3.Higher—order languages 4.Basic syntax 5.Notationalconventions 6.Propositional semantics 7.Propositional tableaux 8.The Elimination Theorem for propositional tableaux 9.Completeness of propositional tableaux 10.The propositional calculus 11.The propositional calculus and tableaux 12.Weak completeness of the propositional calculus 13.Strong completeness of the propositional calculus 14.Propositional logic based on□and ∧ 15.Propositionallogic based on □ ， →， A and ∨ 16.Historical and bibliographical remarks CHAPTER 2.FIRST—ORDER LOGIC 1.First—order semantrcs 2.Freedom and bondage 3.Substitution 4.Frrst—order tableaux 5.Some "book—keg" lemmas 6.The Elimination Theorem for first—order tableaux 7.Hintikka sets 8.Completeness of first—order tableaux 9.Prenex and Skolem forms 10.Elimination of function symbols 11.Elimination of equality 12.RelatMzation 13.Virtual terms 14.Historical and bibliographical remarks CHAPTER 3.FIRST—ORDER LOOIC （CONTINUED） 1.The first—order predicate calculus 2.The first—order predicate calculus and tableaux 3.Completeness of the first—ordcr predicate calculus 4.First—ordcr logic based on 3 5.What have we achieved？ 6.Historical and bibliographical remarks CHAPrER 4.BOOLEAN ALGEBRAS 1.Lattices 2.Boolean algebras 3.Filters and homomorphisms 4.The Stone Representation Theorem 5.Atoms 6.Duality for homomorphisms and continuous mappings 7.The Rasiowa—Sikorski Theorem 8.Historical and bibliographical remarks CHAPTER 5.MODEL THEORY 1.Basic ideas of model theory 2.The Lowenheim—Skolem Theorems 3.Ultraproducts 4.Completeness and categoricity 5.Lindenbaum algebras 6.Element types and M0—categoricity 7.Indiscernibles and models with automorphisms 8.Historical and bibliographical remarks CHAPTER 6.RECURSION THEORY 1.Basiotation and terrrunology 2.Algorithmic functions and functionals 3.The computer URIM 4.Computable functionals and functions 5.Recursive functionals and functions 6.A stockpile of examples 7.Church's Thesis 8.Recursiveness of computable functionals 9.Functionals with several sequence arguments 10.Fundamental theorems 11.Recursively enumerable sets 12.Diophantine relations 13.The Fibonacci sequence 14.The power function 15.Bounded uruversal quantification 16.The MRDP Theorem and Hilbert's Tenth Problem 17.Historical and bibliographical remarks CHAPTER 7.LOGIC—LIMITATIVE RESULTS 1.General notation and terminology 2.Nonstandard models of Ω 3.Arithmeticity 4.Tarski's Theorem 5.Aomatic theories 6.Baby arithmetic 7.Juruor arithmetic 8.A firutely aomatized theory 9.First—order Pcano arithmetic 10.Undecidability 11.Incompletcness 12.Historical and bibliographical remarks CHAPTER 8.RECURSION THEORY （CONTINUED） 1.The arithmcticalhicrarchy 2.A result conceming Tn 3.Encoded theories 4.Inseparable pairs of sets 5.Productive and creative sets； reducibility 6.One—onc reducibility； rccursive isomorphism 7.Turing degrees 8.Post's problem and its solution 9.Historical and bibliographical remarks CHAPTER 9.INTUITIONISTIC FIRST—ORDER LOGIC 1.Preliminary discussion 2.Philosophical remark 3.Constructive meaning of sentences 4.Constructive interpretations 5.Intuitiorustic tableaux 6.Kripkc's semantics 7.The Elimination Theorem for intuitionistic tableaux 8.Intuitionistic propositional calculus 9.Intuitionistic predicate calculus 10.Completeness 11.Translations from classical to intuitionistic logic 12.The Intcrpolation Theorem 13.Some results in classical logic 14.Historical and bibliographical remarks CHAPTER 10.AXIOMATIC SET THEORY 1.Basic developments Z.Ordinals 3.The Aom of Regularity 4.Cardinality and the Aom of Choice 5.Reflection Principles 6.The formalization of satisfaction 7.Absoluteness 8.Constructible sets 9.The consistency of AC and GCH 10.Problems 11.Historical and bibliographical remarks CHAPTER 11.NONSTANDARD ANALYSIS 1.Enlargements 2.Zermelo structures and their enlargements 3.Filters and monads 4.Topology 5.Topologicalgroups 6.The real numbers 7.A methodological discussion 8.Historical and bibliographical remarks BIBUOGRAPHY GENERAL INDFX INDEX OF SYMBOLS
作者介绍
Y.Choquet-Bruhat是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
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